Question

According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t - 5)^2 + 500 for 0 ≤ t ≤ 10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?a) 5:30 b) 7:00 c) 7:30 d) 8:00 e) 9:00

Answer 1

b) 7.00

Step-by-step explanation:

N( t ) = -20( t - 5 )²

dN/ dt = -20 x 2 ( t - 5 )

For maximum N ( depth )

dN/dt = 0

- 40 ( t - 5 ) = 0

t = 5

So at 2 + 5 = 7 .00 am depth of water reaches its maximum.